A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. View Figure Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. To avoid confusion, take the upward direction to be positive throughout the problem. At the top and bottom of the vertical circle, label the ball's speeds v_t and v_b, and label the corresponding tensions in the string T_t_vec and T_vec_b. T_t_vec and T_b_vec have magnitudes T_t and T_b.

Find T_b - T_t, the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle?

Express the difference in tension in terms of m and g. The quantities v_t and v_b should not appear in your final answer.

I'm not doing your work for you, take a snapshot of the ball and string at the top and bottom of the circle, consider all the force components on the ball, and transfer those to how they would affect the tension of the string (Imagine the forces on a small piece of string between the string and the ball). How are the force components different, what would cause a difference in tension?

Let me know how you get on.

http://www.geocities.com/nk7jaffna/askmehelpdesk/circling2.gif
http://www.geocities.com/nk7jaffna/askmehelpdesk/circling.gif